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**Relation :** Let *A* and *B* be two sets, then a relation R from A to B is a subset of *A ×B*.

Thus, *R* is a relation from A to B . ⇔ R ⊆ A × B

Recall that *A × B *is a set of all ordered pairs whose first member is from the set *A *and second member is from *B *i.e.,

A × B = {(x,y) : x ∈ A and y ∈ B }

If *R* is a relation from a non-empty set *A* to a non-empty set *B *and if (*a, b*) ∈ *R, *then we write *aRb* which is read as *a *is related to *b *by the relation *R. *If (*a, b*) ∉ *R* then we write and we say that *a* is not related to *b* by the relation *R*. In other words, a relation is a set of inputs and outputs, often written as ordered pairs (input, output). We can also represent a relation as a mapping or a graph. For example, a relation can be represented as:

**Mapping diagram of Relation**

A relation can also be represented as: